Experiments Sections 9.1, 9.2, 9.3, 9.4, 9.5 - Lecture 19people.hsc.edu/faculty-staff/robbk/math121/lectures... · 2016-02-17 · Outline 1 Experiments vs. Observation 2 Factors and

ExperimentsSections 9.1, 9.2, 9.3, 9.4, 9.5

Lecture 19

Robb T. Koether

Hampden-Sydney College

Wed, Feb 17, 2016

Robb T. Koether (Hampden-Sydney College) ExperimentsSections 9.1, 9.2, 9.3, 9.4, 9.5 Wed, Feb 17, 2016 1 / 18

Outline

1 Experiments vs. Observation

2 Factors and Treatments

3 Randomized Experiments

4 Assignment


Outline




4 Assignment


Experiments vs. Observation

DefinitionAn observational study observes individuals and measures variableswithout influencing the responses.

DefinitionAn experiment applies a treatment to the individuals and observes ormeasures variables to see the effect of the treatment.

In order to observe a cause-and-effect relationship, an experimentis much better than an observational study.Why?





In order to observe a cause-and-effect relationship, an experimentis much better than an observational study.

Why?





In order to observe a cause-and-effect relationship, an experimentis much better than an observational study.Why?


Outline




4 Assignment


Example

Example (Treatments)In an attempt to determine which of two Statistics books helps thestudents learn better, an experiment was designed.One section of Statistics used the book “Statistics in Practice.”Another section used the book “Basic Statistics.”At the end of the semester, the average final grade of each sectionwas calculated.

What are the explanatory and response variables?Describe the “treatment” applied.


Example

Example (Treatments)In an attempt to determine which of two Statistics books helps thestudents learn better, an experiment was designed.One section of Statistics used the book “Statistics in Practice.”Another section used the book “Basic Statistics.”At the end of the semester, the average final grade of each sectionwas calculated.What are the explanatory and response variables?

Describe the “treatment” applied.


Example

Example (Treatments)In an attempt to determine which of two Statistics books helps thestudents learn better, an experiment was designed.One section of Statistics used the book “Statistics in Practice.”Another section used the book “Basic Statistics.”At the end of the semester, the average final grade of each sectionwas calculated.What are the explanatory and response variables?Describe the “treatment” applied.


Confounded Variables

In the previous example, if a difference in final grades wasobserved, what might be the explanation?

The choice of textbook?The professor?The class size?The time when the class met?Which semester?Background of the students?

We say that the explanatory variable (the textbook) is confoundedby these other variables.




The choice of textbook?

The professor?The class size?The time when the class met?Which semester?Background of the students?





The choice of textbook?The professor?

The class size?The time when the class met?Which semester?Background of the students?





The choice of textbook?The professor?The class size?

The time when the class met?Which semester?Background of the students?





The choice of textbook?The professor?The class size?The time when the class met?

Which semester?Background of the students?





The choice of textbook?The professor?The class size?The time when the class met?Which semester?

Background of the students?













Experiments

Definition (Subjects)In an experiment, the individuals are called subjects.

Definition (Factors)In an experiment, the explanatory variables are called factors.

Definition (Treatment)In an experiment, a treatment is a specific combination of values of thefactors.


Example

Example (Treatments)Suppose we performed the textbook experiment with twoprofessors: Prof. Smith and Prof. Jones.If we used two sections and

Prof. Smith used “Statistics in Practice”Prof. Jones use “Basic Statistics”

How many treatments are there?

Would there be a confounding of variables?


Example

Example (Treatments)Suppose we performed the textbook experiment with twoprofessors: Prof. Smith and Prof. Jones.If we used two sections and

Prof. Smith used “Statistics in Practice”Prof. Jones use “Basic Statistics”

How many treatments are there?Would there be a confounding of variables?


Example

Example (Treatments)If we used four sections and

Each professor taught two sectionsEach professor used one book in one section and the other book inthe other section.


Would there be a confounding of the two explanatory variables?


Example

Example (Treatments)If we used four sections and

Each professor taught two sectionsEach professor used one book in one section and the other book inthe other section.

How many treatments are there?Would there be a confounding of the two explanatory variables?


Example

Example (Treatments)If we used eight sections and

Each professor taught four sectionsEach professor used one book in two sections and the other bookin the other two sections.



Outline




4 Assignment


Definition (Randomized Experiment)A randomized experiment is one in which the subjects are assigned atrandom to the different groups.

Why use a randomized experiment?


Definition (Randomized Experiment)A randomized experiment is one in which the subjects are assigned atrandom to the different groups.

Why use a randomized experiment?


Example

Example (Randomized Experiment)Suppose we used four sections and the design

Prof.Smith

Statisticsin Practice

BasicStatistics

Prof.Jones

25 25

25 25

We could randomly assign a total of 100 students to the fourtreatments.Describe exactly how we would do that.


Example

Example (Randomized Experiment)There is more than one way.

One possibility:

Number the students 1 to 100.Use randInt(1,100) fifty times to assign 50 students to Prof.Smith.The rest go to Prof. Jones.Renumber each group 1 to 50.Use randInt(1,50) twenty-five times to assign 25 students ineach group to “Statistics in Practice.”The rest use “Basic Statistics.”


Example

Example (Randomized Experiment)There is more than one way.One possibility:



Example


Number the students 1 to 100.

Use randInt(1,100) fifty times to assign 50 students to Prof.Smith.The rest go to Prof. Jones.Renumber each group 1 to 50.Use randInt(1,50) twenty-five times to assign 25 students ineach group to “Statistics in Practice.”The rest use “Basic Statistics.”


Example


Number the students 1 to 100.Use randInt(1,100) fifty times to assign 50 students to Prof.Smith.

The rest go to Prof. Jones.Renumber each group 1 to 50.Use randInt(1,50) twenty-five times to assign 25 students ineach group to “Statistics in Practice.”The rest use “Basic Statistics.”


Example


Number the students 1 to 100.Use randInt(1,100) fifty times to assign 50 students to Prof.Smith.The rest go to Prof. Jones.

Renumber each group 1 to 50.Use randInt(1,50) twenty-five times to assign 25 students ineach group to “Statistics in Practice.”The rest use “Basic Statistics.”


Example


Number the students 1 to 100.Use randInt(1,100) fifty times to assign 50 students to Prof.Smith.The rest go to Prof. Jones.Renumber each group 1 to 50.

Use randInt(1,50) twenty-five times to assign 25 students ineach group to “Statistics in Practice.”The rest use “Basic Statistics.”


Example


Number the students 1 to 100.Use randInt(1,100) fifty times to assign 50 students to Prof.Smith.The rest go to Prof. Jones.Renumber each group 1 to 50.Use randInt(1,50) twenty-five times to assign 25 students ineach group to “Statistics in Practice.”

The rest use “Basic Statistics.”


Example




Randomized Experiments

Would the randomized design just described eliminate theconfounding of variables?

Why not?What further steps could we take?



Would the randomized design just described eliminate theconfounding of variables?Why not?

What further steps could we take?



Would the randomized design just described eliminate theconfounding of variables?Why not?What further steps could we take?


Outline




4 Assignment


Assignment

AssignmentRead Sections 9.1, 9.2, 9.3, 9.4.Apply Your Knowledge: 1, 2, 4, 5, 10.Check Your Skills: 19, 20, 21, 22.Exercises 29, 31, 32, 33, 34.


Experiments Sections 9.1, 9.2, 9.3, 9.4, 9.5 - Lecture 19people.hsc.edu/faculty-staff/robbk/math121/lectures... · 2016-02-17 · Outline 1 Experiments vs. Observation 2 Factors and

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